Presets
Playback
Station and village
The pump delivers a flow where its head equals the static lift plus the tank head plus the friction loss R Q squared. The tank fills while the pump flow exceeds demand and leakage.
Operation
Model checks
The science
What is modelled
A pump lifts water from a lake to a storage tank on a hill. The tank supplies a village with a constant demand plus leakage, and rain adds a little inflow. The pump head is set by its speed (head scales with speed squared); the flow settles where this head equals what the pipe and the tank ask for. Electric power above the available solar power is counted as grid energy.
Equations
- Operating point:
Hpump = Hstatic + Htank + R Q², withHpump = H0 (n/100)²and the flow capped by the pump capacity. - Tank balance:
dV/dt = Qpump + Qrain - Qdemand, with spill when the tank is full. - Hydraulic power:
P = ρ g Q H / η.
Checks run in the page
- The pump flow solves the operating-point equation at three tank levels.
- A 24-hour water balance: final volume = start + pumped + rain - served - spilled.
- A pure drain test (pump off, no rain) against the exact linear fall V0 - (demand + leak) t.
Honest simplifications
The pump curve is flat (constant head at a given speed) rather than a measured head-flow curve; the tank head is a simple 0-12 m ramp with volume; demand is constant (or x 1.8), not a daily profile; there are no pipe transients and no efficiency curve.
What to try
- Pick Dry summer and watch the tank volume fall below the 150 m3 reserve.
- Lower the pump speed and see the flat pump line sink towards the system curves in the second graph: less flow, less power.
- Raise the solar power until the pink power curve stays under the yellow line: no grid energy is bought.